# Table 10b: Joint Permutation Tests for Income Structure

CA/GDP. 1000 random country orderings. Tests whether the income-ordered coefficient path is *jointly* different from random orderings, not just at individual steps.

| Statistic | Income-ordered | p-value |
|:---|---:|---:|
| Mean Z₁ (AUC) | 27.380 | 0.0990† |
| Fraction above median | 0.750 | 0.3090 |
| Maximum Z₁ | 46.307 | 0.3010 |
| Weighted mean (early emphasis) | 36.031 | 0.1490 |
| Fisher combined | 29.654 | 0.0199\* |
| Declining slope | -6.185 | 0.1880 |

**Interpretation**: Under H₀, income ordering is no different from random. The mean Z₁ across the path, the fraction of steps above the random median, and the Fisher combined rank test all assess whether the income-ordered path is *consistently* elevated — not just at one step.

**Per-step percentile ranks**: 78%, 79%, 91%, 91%, 98%, 47%, 84%, 31%

**Mean rank**: 74.9% (50% under H₀)